I can not think of any situation where one would say 'A man is at the door' It just doesn't sound natural. As far as 'There is the camera on the table', I can think of one unlikely scenario where this would be OK. Suppose someone was searching for several things in the house but could not find the camera he was looking for. A friend could well say: 'There's the camera - on the table' but it would have to have the pause in it that I've indicated.
I love these questions - keep 'em coming!